Continuity mistake: Towards the end of the episode, Ross and Chandler come into Monica's apartment and Ross asks where Rachel is. Watch the objects in Monica's hands, in the shot from behind she puts them on the table, and then does it again in the shot from the front.
Plot hole: Judy says that both her parents died very young. However, we saw her mother's death in "The One Where Nana Dies Twice" and she was quite old. Also, in Season 7, 'TOW Phoebe's cookies', Jack Geller tells Chandler that his father in law still thinks he is a lawyer and says "So if you ever see me giving them legal advice, just nod along," implying that Judy's parents were both still alive.
Continuity mistake: When Charlie and Benjamin are at the restaurant, Benjamin says "I can't believe you chose this restaurant. You remember that night?" To which Charlie replies "I can't believe they let us back in here." However in "The One with the Fertility Test" Charlie has never been to New York before.
Continuity mistake: At the end of this episode, Ross enters the door of Joey's apartment and finds Rachel and Joey kissing. Rachel says "I'm so sorry". The next episode, The One When Ross Is Fine, shows the same scene but it has been changed: Rachel never says "I'm so sorry". Joey starts talking when Ross enters the room.
Visible crew/equipment: After Ross goes in for his disastrous tan, when it cuts to Joey and Rachel walking into their apartment the hole (used for a camera angle) in the wall can be seen at the right side of the screen. As an aside, when Ross leaves Monica and Chandler's apartment later just as Rachel walks in, that hole is seen in the hallway and it's covered up.
Visible crew/equipment: After Chandler starts removing Monica's braids from the shower curtain rings, when it cuts to Joey and Rachel walking into their apartment, we can see the hole in the wall at the right side of the screen. And it's seen again when Ross walks in on Rachel and Joey kissing.
Other mistake: When Chandler, Monica and Erika arrive back at the apartment after sightseeing, Chandler enters the apartment from the left (past where their apartment door is) rather than from the right, as if he came up the stairs. He obviously is entering from the stage and didn't take the time or cue to appear to enter from the direction of the stairs.